Design and configurations of Model A and Model B

U x k x

(2.2)

Where k is the oscillator spring stiffness coefficient, the oscillator system is nonlinear. The potential energy of a nonlinear oscillator could not be considered to be only proportional to a quadratic of the displacement. For the potential energy function U(x), there are some expressions reported in the literature (Pellegrini, S. P., et al., 2012), which is given by

n coefficient of the oscillator. For a Duffing-type oscillator, the potential energy function can be defined as:

Where k1 is the oscillator spring stiffness coefficient of the linear displacement term; k3 is F.

k1 and k3 are the potential energy coefficients of the nonlinear oscillator.

2.2. Design and configurations of Model A and Model B

The general idea behind these devices is that the tube moving back and forth will cause the magnets to pass the coils which will cut the magnetic flux to produce electrical current.

For the design configuration of Model A, a cylindrical tube electromagnetic energy harvester was designed and constructed as shown in Figure 2.1. Two disks of 5 mm thick, 96 mm

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diameter which has inserted 20 Halbach array cube magnets relatively slide in the tube. The two disks were separated and tied together by 5 stacks of magnets. A 100 mm diameter and 200 mm length PVC tube was used to house the assembly of the disks and the support the guide rods. The PVC tube was designed to have two end caps where the two support/guide rods were fixed by the end threads of the rods and nuts. For this linear oscillator, two identical steel springs were used to connect the disks and the end-caps of the tube. In this case, one spring was used to connect one disk at one end and one end cap at the other end. The other spring was used to connect the other disk to the other end cap of the tube. These springs are symmetrically installed on both the sides of the tube. The disk assembly inside the tube formed the magnet oscillator which would hover on the rods and rebound for oscillation.

Model B is designed to include a 3D printed cuboid box (114 mm*132 mm*132 mm) with an end cap and a wooden box frame. The end cap is connected to the cuboid box by four screws. Four pulley wheels are fixed onto the top and bottom inner side walls of the wooden box frame. Two pulleys on the same top or bottom inner wall of wooden box are separated by 254 mm. One rope end of the pulley wheel is connected to the cuboid box, the other end of the rope of the pulley wheel is connected to the coil frame where the coils are wired, which increases the relative speed of the magnets with respect to the coils. There are four large magnet frame carriers highlighted in red colour which are inserted into the four grooves of the white cuboid body as shown in as shown in Figure 4.4 which form a large rectangular magnet frames. The small magnet frame is built in the body of the white cuboid box at the core. There are two types of magnets in the design. One is the induction magnets which are used to induce electricity in the coils, the other is the impinging magnets which are used develop the magnetic springs from the repelling magnetic field forces. Four small or four large induction magnet arrays are fitted into the four slots of the small or large rectangular

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magnet frames. Five magnets in each of the small or four large induction magnet arrays are axially stacked and arranged in the Halbach array in order to generate higher magnet flux density around the coils. In the axial direction of the cuboid box, there are five layers of magnets, each layer of the induction magnets has four small induction magnets and four larger induction magnets which form inner and outer rectangles. The small rectangular tube magnet frame fitted with 20 small neodymium magnets (10 mm x10 mm x 30 mm) is contained within the core of the coil frame. The coil frame wired with two coils is contained within the core of the large rectangular magnet frame which is fitted with 20 big neodymium magnets (10 mm x10 mm x50 mm). The lateral gaps between the coil frame and the small or large rectangular magnet frame is 7.5 mm. There are two coils wired onto the coil frame.

Each of the coils has 200 turns. The height of each of the coils is around 10 mm that is equal to the height of magnets and equal to a quarter of magnetic flux period length which is 40 mm. The wiring direction of the coil is perpendicular to and across the direction of the magnetic fluxes to induce electricity from the relative motion of the induction magnets.

The coil frame was positioned in between the small induction magnets and induction large magnets or between the small and large rectangular magnet frames. Two round disk impinging magnets are placed on the left and right hand sides of the cuboid box at the center and two same round disk impinging magnets are placed on both the left and right hand inner sides of the wooden box frame at the center. The round disk impinging magnets on the cuboid box and the wooden box frame are oriented with the same polarity facing to each other, which generates the expelling magnetic field forces as shown in Figure 2.2 and Figure 2.3.

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Figure 2.1 Geometry of Model A device assembly

Figure 2.2 Geometry of Model B device assembly

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Figure 2.3 Explosion view of the Model B device assembly.